How Canadian lotteries stack up against the Powerball

TORONTO – Canadians disappointed at losing out on last week’s US$1.6 billion Powerball jackpot may want to play closer to home, where a number of lotteries not only have better odds but also better value.

Anyone with a ticket for the record-high prize last week had merely a one in more than 292 million chance to win.

To put that in perspective, someone who purchases 50 tickets weekly would win the jackpot, on average, once every 112,000 years, said Mike Orkin, a former statistics professor and author of “What Are The Odds?”

But odds are only one way to determine whether to play. The size of the jackpot and the cost of the ticket help determine what’s known as the expected percentage return of a lottery.

“That’s the best way to look at how good a lottery is,” said Shannon Ezzat, a mathematics professor at St. Francis Xavier University in Antigonish, N.S.

For the Powerball, like many other U.S.-government run lotteries, people who play over long periods of time can generally expect to make 50 cents on every dollar spent, said Orkin.

“In other words, you’ll lose 50 per cent of your investment.”

Similar Canadian lotteries can offer a slightly better return, partially because winnings aren’t taxed. In the U.S., winnings can be taxed up to 50 per cent.

“That really reduces your expected values,” Ezzat said, which are likely lower than 50 per cent for the Powerball after factoring in taxes.

Lotto Max and Lotto 6/49, on the other hand, generally hover between 40 and 60 per cent, Ezzat said.

But the risk of multiple winners, which increases as more tickets are sold, can lower those numbers.

For example, a single Lotto 6/49 ticket stands a one in nearly 14 million chance of winning. But if 28 million tickets are sold, said Ezzat, it’s more likely there will be two winners splitting the jackpot, which lowers the expected percentage value of each ticket.

Charity fundraisers, meantime, sell more expensive tickets but boast better odds. Among the dozens of charity lotteries, the Heart & Stroke Foundation’s lottery claims that roughly one in two tickets wins a prize.

But these lotteries generally don’t provide better expected values than provincial games of chance, Ezzat said, because tickets for these types of lotteries are generally expensive — $100 or more — and the prize values vary. The Heart & Stroke Foundation’s prizes include $1 million, luxury cars or simply $25, $50 or $100 cash.

Rather than buying one ticket, Ezzat said some bulk ticket packages — like the Sick Kids lottery’s 20 tickets for $900 — can turn into a good deal if purchased with 19 other people. The expected percentage return per ticket, in that case, is 87, he said.

There are also fundraising lotteries, including Chase the Ace. The odds for Chase the Ace, a popular lottery made famous by a recent $1.7-million jackpot in Inverness, N.S., seem to increase the longer the game lasts.

It has two parts: a lottery, which then gives the winner the chance to draw the ace of spades from a deck of cards for a bigger chunk of the jackpot. The expected percentage return increases as fewer cards remain, Ezzat said.

“In some sense, the people who play early are subsidizing the people who get in later,” he said.

The only time Ezzat has ever calculated a positive expected percentage return in any lottery was for Inverness’s final draw last year, when organizers pledged to continue selecting tickets until someone pulled the ace from a remaining five cards to end the game.

For anyone with a ticket that day, the expected percentage return totalled 121 per cent, he said. This means, if someone played the game billions of times, they would earn on average $1.21 for every dollar spent.

So-called 50/50 draws, meantime — where the winner pockets half the ticket sales — are a popular fixture at Canadian sporting events.

But unless the organizers offer discounted bulk tickets, the expected percentage return is always 50 per cent, said Ezzat.

“There’s no benefit in getting in early,” he said. “It doesn’t matter.”

But while the odds fluctuate based on the game, Orkin said, there’s really few good reasons to play any lottery.

There’s the profoundly slim chance of changing one’s life with a massive payoff from a small investment, he said, but — so long as there’s no gambling problem — “it’s worth it to go out and buy a couple of lottery tickets, especially when the jackpot gets high, if you find it entertaining.”